For most travelers, the Bridger Range is little more than a sight in the distance as one drives along U.S. 89 between I-90 and White Sulphur Springs.
From your location, get to MT 86; its southern end is near Bozeman, and its northern end is on U.S. 89 south of White Sulphur Springs.
Around MP 21, turn onto a road signed for access to Fairy Lake. Follow signs for Fairy Lake and drive about 6 miles to two obvious campsites on the left side of the road. Just past the sites and on the other side of the road is a trail heading up a meadow; that is the start of the approach.
Hike up the trail, which gets really steep in places. As you near the obvious saddle, cut up and left before you reach a large patch of trees. Gain the ridge and then find a steep, loose gully leading to a basin well above Frazier Lake. Descend the gully and cut left to the base of the East Buttress.
Since the return will take you back to the top of the gully or close to it, you might want to leave anything you don't absolutely need here.
The East Buttress has two established routes at this time:
Nothing special; read and follow posted regulations.
Late spring through early fall.
Camp at Fairy Lake, the sites by the approach trail, or in dispersed sites.